solve by equation.no hit and trial?

Question

a^b-b^a=b-a

Answer 1

a=1, b=1

Answer 2

With two unknowns, this can't be solved by equation without having a second equation. Then, you could solve for one variable in terms of the other and make a substitution to get down to one variable. However, one possible answer is a = b = 0. Why? Anything raised to the zero power is 1. So, you'd have 1 - 1 = 0 - 0 which is a true statement.